Question

The equation of a circle whose $x$-coordinate of the centre is $5$ and radius is $4$ units and also touches the $x$-axis, is

• A. $x^2+y^2-10x+8y+49=0$
• B. $x^2+y^2-10x-8y+25=0$
• C. $x^2+y^2+8x-10y+25=0$
• D. $x^2+y^2-16x-9y-25=0$

Answer 1

The correct option is B $x^2+y^2-10x-8y+25=0$


The required equation of the circle whose $x$-coordinate of the centre is $5$ and radius is $4$ units also touches the $x$-axis is $(x-5{)}^2+(y-4{)}^2=4^2$ [Since radius is equal to the $y$-coordinate of the centre]
$\Rightarrow x^2-10x+25+y^2-8y+16=16$
$\Rightarrow x^2+y^2-10x-8y+25=0$